Find the sum of all odd positive integers less than 450.

Find the sum of all odd positive integers less than 450.
Solution :
By wring the odd positive numbers less than 450, we get 
1, 3, 5, 7, ...........447,449
1 + 3 + 5 + 7 +............. + 447 + 449
a = 1, d = 3 - 1  = 2, l = 449
Sn  = (n/2)[a + l]
n = [(l - a)/d] + 1
n = [(449 - 1)/2] + 1
 =  (448/2) + 1
n  = 225
Sn  = (225/2)[1 + 449]
=  (225/2) 450
S225  =  50625

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